Exercise Set 10
AARON'S PORTFOLIO

Aaron Rodgers is interested in selecting an investment portfolio. Since you are his financial advisor, he comes to you. You determine that Mr. Rodgers' preferences regarding expected return (E) and risk (σ) are represented by the utility function: u(E,σ) = 5E - 3σ2. Furthermore, you determine the equation of the efficient frontier to be: E - σ0.5 = 4.

Now answer the following questions.

  1. Obtain the first-order partial derivatives U1(E,σ) and U2(E,σ). What does each represent? Why is U2 negative?
  2. Sketch an indifference curve, with E on the vertical axis.
    1. Show that it has a positive slope. What is the slope dE/dσ equal to?
    2. Intuitively, why is the slope positive?
    3. Sketch another indifference curve that is roughly parallel to the first one. Which one represents a greater level of utility? Why?
  3. Use FOCs and SOCs to obtain Mr. Rodgers' optimal portfolio. What is the expected return and risk associated with it? What is Rodgers' maximum utility?
  4. Sketch the efficient frontier. Indicate the optimal point by sketching Rodgers' "highest" indifference curve.
  5. If Rodgers became more risk-averse, how would his optimal portfolio change? [Hint: What will happen to the shape of the indifference curves?]
  6. Does Mr. Rodgers give you free tickets to the Packer games?
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